The essential boundary of certain sets
Andrew M. Bruckner, Roy O. Davies, Casper Goffman · Proceedings of the American Mathematical Society · 1986
The essential boundary of a measurable set is related to the de Giorgi perimeter and was introduced by Vol’pert in his "improvement" of Federer’s work. For a totally disconnected compact set of positive measure in n n space the essential boundary can be of Hausdorff n − 1 n - 1 dimension but cannot have σ \sigma finite ( n − 1 ) (n - 1) -measure.